Paramus itself might not be a bad fit. It's a very suburban feeling place with a few malls, strip malls, so lots of places to shop and dine within the town. If you want a town with more of a "main street USA" type of a feel, you can try Westwood, which is just north of Paramus, or Ridgewood, which is just west of Paramus. Both of these towns have a few restaurants and shops on their main streets and train stations where you can take a train to Hoboken/NYC, and are only a 5-10 min drive to parts of Paramus. All of these places, and most other towns in northern Bergen County are generally very safe, family-oriented suburban communities.
If you're looking at ads on craigslist and other sites, the only towns near Paramus I'd caution you about are Hackensack (just south of Paramus) and Paterson (southwest of Paramus, a few towns over). Hackensack has some OK areas and some not OK areas, so if your search leads you there, check back in for advice on what areas of that town to avoid or target.
Bergen County has "blue laws" which require that retail establishments be closed on Sundays. This is a "you love it or you hate it" thing. The benefit of blue laws are that there's one day a week without much traffic (and in Paramus, which has a lot of malls, this can be a blessing), but it makes life a little less convenient if you want to run your personal errands on a Sunday.
The gas thing is simple. When you pull up to the pump, just hand the attendant your credit card or cash and tell him/her how much and what kind of gas you want (i.e., "fill it up, regular" or "$20, supreme"). You don't tip them. Years ago attendants would ask if you want them to check your oil or clean your windshield, in which case I would offer a tip sometimes. But they rarely do that anymore.
Car insurance is expensive in NJ. The only other thing I'd warn you about is that many of our highways were built in the 1930s-1950s. Things like exit ramps, acceleration lanes, etc. are sometimes sub-standard and inconsistent. For example, an exit ramp built in the 1980s through today would have a nice long acceleration lane at the end, so you can speed up on the end of the ramp to merge into traffic. Ramps built in the 50s might have a stop sign at the end, with no space to merge at full speed. So never expect that the highway you're driving on has modern specs.
Oh, and another Jersey thing is jughandles. On many high-traffic roads, all turns are made from the right. There's no left-turn lane. The purpose of this is to reduce the number of sequences in a traffic light cycle, thereby giving each movement the maximum green time possible. It's a little confusing for newcomers and visitors who aren't used to it.
Jughandle - Wikipedia, the free encyclopedia